A RFID system is a technology for detecting information on an object through wireless communication between a tag on the object and a reader, and its applications are being expanded to various areas. Because of its wireless communication, however, there are many vulnerabilities in security. Until now, many studies have been executed in order to solve problems related to the security and stability of RFID. In order to resolve vulnerabilities in existing security methods for privacy protection, this study proposed an authentication protocol that uses hash values received from tags and random numbers. When the proposed protocol was implemented, it was safe from various types of attacks between tag and reader and between reader and DB. Furthermore, compared to recently proposed protocols, it could implement a RFID system with enhanced security and less computation in tags.